The common stock of Leaning Tower of Pita, Inc., a restaurant chain, will generate the following payoffs to investors next year: State Boom Normal Economy Recession Dividend $5 $2 0 Stock Price $195 $100 0 The company goes out of business if a recession hits. Calculate the expected rate of return and standard deviation of return to Leaning Tower of Pita shareholders. Assume for simplicity that the three possible states of the economy are equally likely. The stock is selling
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Risk and return
Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.
Capital Asset Pricing Model
Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.
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- Problem 2. The stock of Business Adventures sells for $40 a share. Its likely dividend payout at the end-of-year price depends on the state of the economy by the end of the year as follows: State of the Economy Stock Price Recession Normal Growth Boom $34 $43 $50 Dividend $ 0.50 $ 1.00 $ 2.00 (a) Calculate the expected holding-period return and standard deviation of the return. All three scenarios are equally likely. (b) Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury Bills. The return on Treasury Bills is 4%. = (c) Assume your utility function is U(u, o) = μ-302. How much would you invest in the stock and how much would you invest in T-Bills?a company will generate payoffs to investors the following year which depend on state of economy as follows: dividend stock price boom $8 $240 normal economy 4 90 recession 0 0 company goes out of business if a recession hits, calculate expected rate of return and standard deviation of return to shareholders and assume for simplicity that the three possible states of the economy are equally likely. The stock selling today goes for $80Self-Test Problem Given are the following possible dollar returns (dividends plus capital gains) over the coming year from a $10,000 investment in General Motors common stock: State of Economy Probability 0.20 0.60 Return $-1,000 1,500 2,500 Recession Normal year Boom 0.20 Convert the dollar returns to percentage returns and then determine the a. Expected return b. Standard deviation of returns
- 15. Scenario Analysis and Portfolio Risk. The common stock of Leaning Tower of Pita Inc., a restaurant chain, will generate payoffs to investors next year, which depend on the state of the economy, as follows: (LO11-2 and LO11-3) Dividend Stock Price Вoom $8 $240 Normal economy 4 90 Recession a. The company goes out of business if a recession hits. Calculate the expected rate of return and standard deviation of return to Leaning Tower of Pita shareholders. Assume for simplic- ity that the three possible states of the economy are equally likely. The stock is selling today for $80. b. Who would view the stock of Leaning Tower of Pita as a risk-reducing investment-the owner of a gambling casino or a successful bankruptcy lawyer? Explain.5 The stock of Business Adventures sells for $50 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: Boom Normal economy Recession Expecte return Standard deviation Dividend $ 3.00 1.20 0.75 Required: a. Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Stock Price $ 60 58 49 Expected return Standard deviation. % % b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 5%. (Do not round intermediate calculations. Round your answers to 2 decimal places.) % %4.StockA sells for $40 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: Probability Stock Price Boom $50 Normal economy 42 Recession 30 50% 30% 20% Dividend $2.00 1.00 0.50 a.Calculate the expected holding-period return and standard deviation of the holding period return. b.Calculate the expected return and standard deviation of a portfolio invested half in this stock and half in Treasury bills. The return on bills is 4%.
- 36.Given the following possible returns (dividends plus capital gains) over the coming year from P100,000 investment in General Motors common stock: State of Economy Profitability ReturnRecession 0.20 P-1,000 Normal year 0.60 1,500Boom 0.20 2,500What is the expected return?Assume that Conrado Corporation is considering the possible rates of return it might earn next year on a P100,000 investment on the stocks of Buenos Aires or a P75,000 on those of Jessa. The future returns 3.2 depend on the state of the economy with their corresponding probability distribution. Stock Jessa Return (r) Stock Buenos Aires State of Economy Bad Probability (p) Probability (p) 20% Return (r) -8% 15% -10% Normal 15% 70% 20% 80% Good 35% 15% 40% 20% 1. What is the Expected Return of Stock Buenos Aires? 2. What is the Expected Return of Stock Jessa? 3. What is the Variance of Stock Buenos Aires? 4. What is the Variance of Stock Jessa? 5. What is the Standard Deviation of Stock Buenos Aires? 6. What is the Standard Deviation of Stock Jessa? 7. What is the Coefficient of Variation of Stock Buenos Aires? 8. What is the Coefficient of Variation of Stock Jessa?The stock of Business Adventures sells for $40 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: Boom Normal economy Recession Expected return Standard deviation Dividend $ 2.80 1.80 0.90 Required: a. Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected return Standard deviation Stock Price $ 48 43 34 b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 5%. (Do not round intermediate calculations. Round your answers to 2 decimal places.) % %
- Assume that the economy can experience high growth, normal growth, or recession. Under these conditions, you expect the following stock market returns for the coming year: State of the Economy High Growth Normal Growth Recession Probability 0.2 0.7 0.1 Return 60% 18% 2% a. Compute the expected value of a $1,000 investment over the coming year. If you invest $1,000 today, how much money do you expect to have next year? What is the percentage expected rate of return? Instructions: Enter dollar values rounded to the nearest whole dollar and percentages rounded to one decimal place. The expected value is $ and the expected rate of return is b. Compute the standard deviation of the percentage return over the coming year. Standard deviation = % = %. c. If the risk-free return is 7 percent, what is the risk premium for a stock market investment? Risk premium %Subject: Corporate finance You have just inherited DKK 200,000, which you are going to invest in stocks. You are considering two stocks, DJH and SDR. The two stocks have the following returns during economic growth and economic recession: Economic growth Economic recession Stock DJH 0% 10% Stock SDR 15% -5% a) What is the expected return and standard deviation for stocks DJH and SDR? b) You consider buying both stock DJH and SDR. What is the expected return and standard deviation of your portfolio if you: ba. Invest DKK 6,000 in DJH and DKK 14,000 in SDR? bb. Invest DKK 10,000 in DJH and DKK 10,000 in SDR? bc. Invest DKK 14,000 in DJH and DKK 6,000 in SDR? bd. Invest DKK 18,000 in DJH and DKK 2,000 in stock SDR? c) You realize that the four portfolios above have different standard deviations. Explain intuitively why this is the case (1 to 10 sentences). d) Which of the four portfolios would you choose to invest in? Why?3. The stock of Business Adventures sells for $100 per share. Its likely dividend payout and end-of year price depend on the state of the economy by the end of the year as follows: Boom Normal economy Recession Dividend $2.00 $1.00 $0.00 a. Calculate the expected holding period return and standard deviation of the holding-period return. Probability of Scenario 0.5 0.25 0.25 b. Stock Price $150 $115 $84 Calculate the expected return and standard deviation of a complete portfolio invested 60% in Business Adventures and 40% in Treasury bills. The return on the T-bill is 3%.